In this article we first set up the relativistic orbit equation for a
particle in a central potential presumed to be dependent on the radial
coordinate only. The relativistic central force orbits were previously
studied in Refs. [1]}, [2]}, [3]}, [4]}. A brief
description of the central force problem in a relativistic setting in
a Coulomb potential was presented in the book on classical theory of
fields by Landau and Lifshitz [5]}. Before one starts the
main analysis about the stability of orbits of relativistic particles
in a central force potential it is better to specify the assumptions
one makes in arriving at definite results. In the present article we
use the same assumptions and the approximations as utilized by Boyer
in Ref. [1]} and Landau in Ref. [5]}. In the
specific references cited above, none of them present a Lorentz
covariant treatment of the relativistic central force problem. The
main reason being that all of them assumes a central potential \(V(r)\) 
where \(r=|{\bf r}|\)  is the distance between the source and the
orbiting particle. The form of the potential only depends on the
position coordinates of the orbiting particle. The form of \(V(r)\)  is
not Lorentz covariant. In such cases the results of the whole analysis
is valid in a particular frame where the origin of the coordinate
system coincides with the potential center.
